Non-local Means using Adaptive Weight Thresholding

Asif Khan and Mahmoud R. El-Sakka

Computer Science Department, The University of Western Ontario, London, Ontario, Canada

Keywords:

Image Denoising, Additive Gaussian Noise, Non-local Means, Two-stage Non-local Means, Spatial Domain

Denoising.

Abstract:

Non-local means (NLM) is a popular image denoising scheme for reducing additive Gaussian noise. It uses

a patch-based approach to ﬁnd similar regions within a search neighborhood and estimates the denoised pixel

based on the weighted average of all pixels in the neighborhood. All weights are considered for averaging,

irrespective of the value of the weights. This paper proposes an improved variant of the original NLM scheme

by thresholding the weights of the pixels within the search neighborhood, where the thresholded weights are

used in the averaging step. The threshold value is adapted based on the noise level of a given image. The

proposed method is used as a two-step approach for image denoising. In the ﬁrst step the proposed method is

applied to generate a basic estimate of the denoised image. The second step applies the proposed method once

more but with different smoothing strength. Experiments show that the denoising performance of the proposed

method is better than that of the original NLM scheme, and its variants. It also outperforms the state-of-the-art

image denoising scheme, BM3D, but only at low noise levels (σ ≤ 80).

1 INTRODUCTION

Image denoising is the process of reducing noise ar-

tifacts from a digital image and it is one of the most

fundamental problems in image processing. Noise is

a random signal which affects the signal from the ac-

tual source by adding unwanted information to the

signal. In digital image, noise causes random varia-

tion of brightness or color. It is usually produced dur-

ing the image acquisition phase, caused by the sen-

sors of digital cameras or scanners. Modern digital

cameras have come a long way in using high quality

sensors which have signiﬁcantly reduced the presence

of noise during image acquisition, but still noise can

affect an image especially in low light conditions.

Noise in digital images can be categorized either

as additive or multiplicative noise. Additive noise

gets added with the image signal. It is modeled as:

v(i) = u(i) + η(i) (1)

where v(i) is the observed intensity value at pixel i,

u(i) is the actual raw intensity value and η(i) is the

random noise affecting pixel i. Multiplicative noise

signal gets multiplied in the original image source. It

is modeled as:

v(i) = u(i) × η(i) (2)

The main challenge of a denoising model is to re-

duce noise while preserving the texture, ﬁne details

and edges of an image. A model which is able to re-

duce signiﬁcant noise artifacts but completely blurs

the entire image, to a point where only minimal visual

information can be extracted, is not ideal. Similarly, a

denoising method which preserves the textures in the

image but fails to reduce the noise to a satisfactory

level is not an effective model as well.

The denoising methods can be generally catego-

rized as either spatial domain approaches or trans-

form domain approaches. The term spatial domain

refers to the image plane itself (Gonzalez and Woods,

2008) and the methods under this domain uses the raw

intensity of the pixels to generate a denoised image.

In transform domain approaches, the image is trans-

formed to another domain, e.g., frequency domain us-

ing, for example, Fourier transform or wavelet trans-

form. The transform domain decomposes smooth re-

gions in an image into low frequencies, while edges

and subtle information into high frequencies, thus

making it easier to target and enhance certain regions

in an image.

Among the various noise types, additive white

Gaussian noise has attracted signiﬁcant interest

among researchers in the past few decades. Our work

will focus only on this type of noise reduction. Ad-

ditive white Gaussian noise is referred to noise sig-

nals with a zero-mean Gaussian distribution, having

Khan, A. and El-Sakka, M.

Non-local Means using Adaptive Weight Thresholding.

DOI: 10.5220/0005787100670076

In Proceedings of the 11th Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2016) - Volume 3: VISAPP, pages 69-78

ISBN: 978-989-758-175-5

uniform power across the frequency band. Initial ap-

proaches to reduce the additive Gaussian noise in-

cluded the use of basic linear ﬁlters, namely mean

ﬁlter, median ﬁlter and Gaussian smoothing (Gonza-

lez and Woods, 2008). These ﬁltering approaches use

only the raw pixel values in a small local neighbor-

hood around each pixels to determine the denoised

image. These methods does not take into account

the extent to which the neighborhood overlaps with

smooth or textured regions. Thus the use of such lin-

ear ﬁlters are detrimental for edge and texture preser-

vation, resulting in blurry denoised images. To ad-

dress this problem, Perona and Malik proposed an

iterative edge preserving method called Anisotropic

Diffusion (Perona and Malik, 1990). It attempts to

determine whether a pixel is part of a smooth or a tex-

tured region and applies differentdegree of smoothing

based on the characteristics of its locality.

Most of the earlier spatial domain denoising meth-

ods used pixel intensities within a deﬁned local

neighborhood around each pixel for estimating a de-

noised version of a noisy image. In recent years,

Buades et el. proposed a non-local, patch based

approach called Non-Local Means (NLM) (Buades

et al., 2005a)(Buades et al., 2005b). It takes advan-

tage of the fact that similar local regions can be spread

through out the entire image. Each of the pixels are

denoised using a weighted average of all the pixels

within a deﬁned search area. The weights are as-

signed based on the local characteristics of the pixels

used in the weighted averaging step. It uses weighted

euclidean distance of the local region around the pixel

being denoised, also referred to as the reference patch,

and the local regions around each of the the pixels

within the search area. The patches with smaller eu-

clidean distance, i.e., patches similar to the reference

patch are assigned higher weights.

The concept of non-local based approach has also

been applied to denoising methods in frequency do-

main. Dabov et el. proposed Block Matching and 3D

Filtering (BM3D) (Dabov et al., 2007), using patch

based concept for image denoising. It is a two-step

process, where the ﬁrst step groups similar patches

into blocks, followed by a transform operation and

hard thresholding of the transform coefﬁcients to gen-

erate a basic estimate of the denoised image. The

basic estimate is used in the second step to generate

the actual denoised image. BM3D is one of the state-

of-the-art approaches for denoising additive Gaussian

noise.

In the ﬁeld of spatial domain denoising, non-local

means demonstrated signiﬁcant improvement in de-

noising images affected with additive Gaussian noise

and researchers have continued further work on the

method and have proposed improvements for it. The

exhaustive search nature of non-local means makes

it computationally expensive. To improve the com-

putation cost, several methods have been proposed.

Tasdizen used principal component analysis (PCA) in

conjunction with non-local means (Tasdizen, 2008).

The image neighborhoods are projects to a lower di-

mension space using PCA and the reduced subspace

is used for computing similarities. A similar dimen-

sion reduction approach has also been proposed by

Maruf and El-Sakka (Maruf and El-Sakka, 2015),

where the image neighborhood are projected to a

lower dimension by using t-test.

Along with the research focused on improving the

computation performance of non-local means, work

has also been done on improving the denoising perfor-

mance as well. Rehman and Wang proposed SSIM-

based non-local means (Rehman and Wang, 2011),

utilizing structural similarity instead of euclidean dis-

tance when comparing local characteristics between

patches. Chaudhury and Singer proposed Non-Local

Euclidean Medians (Chaudhury and Singer, 2012),

replacing the use of mean with median. Zhu et el.

proposed a two-stage non-local means approach with

adaptive smoothing parameters (Zhu et al., 2014). It

generates a basic denoised image by applying NLM

in the ﬁrst stage and the basic image is reﬁned one

more time in the second stage by using NLM but with

smaller smoothing strength.

Non-local means and its variants have been used

in variousimaging applications such as medical imag-

ing, including MRI brain images (Iftikhar et al.,

2013), CT scan imaging (Kelm et al., 2009) and 3D

ultrasound imaging (Hu and Hou, 2011). It is also

used in video denoising (Basavaraja et al., 2010) (Xu

et al., 2010), surface salinity detection (Zhao and

Liu, 2012) and metal artifact detection (Mouton et al.,

2012).

Although much work has been done to improve

non-local means, there are still possibilities for further

improvements. In the weighted averaging step, non-

local means considers all the pixels within a deﬁned

search area. The pixel patches having signiﬁcantly

different details than the patch of the reference pixel

being denoised are likely to deviate the estimated de-

noised value of the reference pixel from its true noise-

free pixel intensity, even with their smaller weights.

In our proposed method we have thresholded the pixel

weights and only the pixels with weight higher than

the cut-off weight are considered for weighted aver-

aging. The threshold is adapted based on the noise

level of the given noisy image. The proposed method

is applied in a two-step approach, where the ﬁrst step

applies the proposed method to generate a basic de-

VISAPP 2016 - International Conference on Computer Vision Theory and Applications

noised image and in the second step the image gen-

erated from the ﬁrst step is again denoised, using

a smaller smoothing parameter. Experiments have

illustrated better denoising performance of the pro-

posed method compared to existing methods, e.g., the

original NLM, a variant of NLM and BM3D, both

in terms of objective measurements and visual image

quality.

2 NON-LOCAL MEANS (NLM)

Buades et el. proposed a non-local based approach for

image denoising (Buades et al., 2005a)(Buades et al.,

2005b). Images have redundant or similar patterns in

them and the Non-Local Means (NLM) approach at-

tempts to take advantage of such self-similarities to

estimate the denoised gray level value of each pixel.

Instead of using only a local region around each pixel

for estimating the actual intensity of the pixel, NLM

uses a non-local approach by searching for similar

patches, within a certain search-bound, in the im-

age. The center pixel of each patch contributes to a

weighted averaging based on the similarity between

the reference and search patches.

When comparing the reference patch to a search

patch, a variation of the euclidean distance is mea-

sured. The euclidean distance measures the sum of

squared difference between each pixel in a patch. To

give more importance to pixels near the center of the

patch, a Gaussian weight distribution is used, thus re-

sulting in the ﬁnal measurement being the weighted

euclidean distance, kN(i) − N( j)k

2,a

, where a is the

standard deviation of the Gaussian kernel and N(i)

and N( j) are the patches around pixel i and j, respec-

tively. The weight associated with each of the search

patches is based on the similarity with the reference

patch. After calculating the euclidean distance be-

tween the patches, the weight is assigned using Equa-

tion (3),

w(i, j) =

Z(i)

−

kv(N

)−v(N

2,a

, (3)

where v(N

) and v(N

) are the gray values of the pixels

in the patch centered on i and j respectively. Z(i) is

the normalizing constant as deﬁned in Equation (4),

Z(i) =

∑

−

kv(N

)−v(N

2,a

(4)

The constant, h, controls the decay rate of the expo-

nential weight function. Given a noisy image, the es-

timated value NL[v](i), for pixel i, is computed as a

weighted average of the center pixels of the patches

in a certain search area, see Equation (5),

NL[v](i) =

∑

j∈I

w(i, j)v( j), (5)

where w(i, j) is the weight calculated based on the

similarity of neighborhood around pixel i and j.

3 NON-LOCAL MEANS USING

ADAPTIVE WEIGHT

THRESHOLDING

Non-local means method deﬁnes a search area of size

S × S centered on the pixel, i, being denoised. The

similarity of all the patches deﬁned around each of

the pixels within the search area is considered during

the weighted averaging process, where higher weights

are assigned to patches which are more similar, as de-

termined by lower euclidean distance to the reference

patch. The goal of the weighted averaging process is

to estimate the true noise-free intensity value of pixel

i, based on the similarity of the patches within the de-

ﬁned search area of the given noisy image. The inclu-

sion of the center pixels of patches which are not very

similar to the reference patch is likely to move the re-

sulting estimate further from the true pixel intensity

value of the noise-free image.

In our proposed method, only a subset of the avail-

able patch centers are considered for the ﬁnal estima-

tion of the denoised pixel. The patches are selected

based on the similarity measure compared to the ref-

erence patch. Effectively, a cut-off weight, w

thresh

selected using a deﬁned percentile position, w

percentile

among the availablepatch weights within the bounded

search area and the weights of the patches are thresh-

olded against w

thresh

. All weights above w

thresh

are

unchanged and weights below w

thresh

are reduced

to zero, thus removing their pixel centers from the

weighted averaging process. The selected percentile

position is determined based on the noise level in a

given image. In real systems, the actual amount of

noise in a noisy image cannot be known beforehand.

The noise can be estimated in digital image using

fuzzy processing (Russo, 2001), image ﬁlters (Mou-

ton et al., 2007) and local variance estimate (Lim,

1990) methods.

For low noise levels, a higher cut-off weight,

thresh

, is selected for thresholding the patch weights

and as the noise level of a given image increases,

thresh

is lowered to include more patch centers for

averaging. For lower noise levels, only the patches

with high similarity measure to a reference patch can

be used to estimate a denoised image. The remaining

Non-local Means using Adaptive Weight Thresholding

patches can be considered as outliers. So, a higher

cut-off threshold is selected for low noise levels. In

high noise, the euclidean distance measurement may

not give a true measure of patch similarity as it will

end up comparing, to some extent, the noise between

patches along with the structures of the patches. So,

considering only the higher weighted patch centers,

by keeping the threshold value high, can in fact devi-

ate the denoised estimation from the true value. To

mitigate this effect, the threshold value is lowered

so that more pixels are averaged for attenuating the

noise. The denoised image is calculated as shown in

Equation (6),

NL[v](i) =

∑

jEI

ˆw(i, j)v( j), (6)

where ˆw(i, j) is the thresholded weight between patch

at pixel i and patch at pixel j as shown in Equation

(7),

ˆw(i, j) =

(

w(i, j), if w(i, j)>w

thresh

0, otherwise

(7)

The proposed method is applied in two-step approach.

In the ﬁrst step, proposed method is used to generate

a basic estimate of the denoised image. In the basic

estimate, most of the noise is reduced but still some

visible noise artifacts remain, especially for stronger

noise levels and it is necessary to further denoise the

basic image for better denoising (Zhang et al., 2010).

As most of the noise is reduced in the basic image,

similar regions can be identiﬁed more easily which

helps to generate better denoised images in the sec-

ond step. In the second step, the basic image is de-

noised using similar method used in the ﬁrst step, but

with a smaller smoothing parameters. To verify that

the two-step approach is good enough, we conducted

experiments to measure the improvement in the de-

noising performance with further steps and found the

amount of improvements to be negligible, and even

less in some cases.

Non-local means has two key parameters, namely

the patch size and the search size. In our proposed

method we have attempted to select the optimal patch

and search window sizes based on the noise level in

the image. We have empirically deﬁned a model for

selecting the patch size and the corresponding search

window size for a noise level, σ, see Section 4.1

4 EXPERIMENTAL RESULTS

In this section we will report the experimental results

of our proposed method. All the experiments were

carried out on the standard Kodak gray-scale image

set. It comprises of 24 gray-scale images of dimen-

sions 768 × 512 and 512 × 768. The Kodak image

set is shown in Figure 1. For the purpose of our

experimentation, the standard noise free image were

contaminated by additive Gaussian white noise, ran-

domly distributed throughout the image. The ﬁnal

intensity values were kept within the maximum in-

tensity value of gray-scale images. The noise lev-

els, determined by σ, ranges from 10 to 100, with

a step size equals 10. The performance of our pro-

posed method is compared with the original non-

local means (NLM), the two-stage non-local means

(TS-NLM) and the Block Matching and 3D Filtering

(BM3D) methods.

4.1 Parameter Selection

The patch size and search window size for a given

noise level was determined empirically, using an iter-

ative learning approach on a training image set. The

training image set is shown in Figure 2. At ﬁrst, the

patch size was ﬁxed and the search window size was

varied, for each noise levels, to select the best search

window size. The noise levels, σ, ranged from 10

to 100, with a step size equals 5. Next, the patch

size was varied for each noise levels, while using the

best search window size for each noise as determined

in the previous step. The best patch size for each

noise level was used to ﬁnd the correspondingoptimal

search window sizes one more time. This process was

repeated until an iteration was reached where updat-

ing the optimal search window size for a noise level

did not change the corresponding best patch size and

vice versa.

From our experiments, we have selected a patch

size of 7 × 7 when the noise strength is, σ ≤ 80 and

for σ>80 the patch size is increased to 9×9. For high

noise levels, the larger patch size is needed to reduce

the effect of noise in patch similarity measurement.

From our experiments, we also determined a

model for selecting the search window size for a noise

level, σ. The model used to select the search size S×S

for a given noise, σ, is shown in Equation (8),

S = round

odd

(0.117σ + 9.758), (8)

where, round

odd

() rounds a decimal value to its near-

est odd integer. As the search window is centered on

pixel, i, being denoised, the search window size needs

to be an odd integer.

For thresholding the weights, the percentile posi-

tion of the weight to be used as the cut-off weight is

given by Equation (9),

percentile

= ceil(100× e

−

100

), (9)

VISAPP 2016 - International Conference on Computer Vision Theory and Applications

(a) Boat2 (b) Lighthouse (c) Woman (d) Sail (e) Statue (f) Model

(g) Beach (h) Bike (i) Bridge (j) Cottage

(k) Door (l) Flower (m) Raft (n) Girl

(o) Hats (p) House2 (q) Houses (r) Windows

(s) Island (t) Lake (u) Landscape (v) Lighthouse2

(w) Parrot (x) Plane

Figure 1: Test Image set (Kodak Image set).

where ceil() rounds a decimal value to the smallest

following integer. The thresholding model deﬁned

by Equation (9) was also empirically found through

learning on the training image set. We applied differ-

ent linear and exponential models to select the thresh-

old. The model which provided the best denoising

Non-local Means using Adaptive Weight Thresholding

(a) Lena (b) Barbara (c) Baboon (d) Boats (e) Peppers

Figure 2: Train Image set.

performance was ﬁnally selected.

The smoothing parameter, h, for the ﬁrst step of

the denoising approach is set as h

basic

= 10σ. For the

second step, h

final

= σ is used as the smoothing pa-

rameter value.

4.2 Performance Measure

To measure the performance of our proposed method

in comparison to other existing denoising methods,

we have used the Peak Signal to Noise Ratio (PSNR)

and the Mean Structural SIMilarity (MSSIM) mea-

sure. These measures are generally used for objec-

tive evaluation and measurement of various denois-

ing methods. We also evaluated subject comparison

between our proposed method and existing denoising

methods.

4.2.1 Peak Signal to Noise Ratio (PSNR)

The Peak Signal to Noise Ratio measures the ratio

between the maximum possible power of a signal to

the power of the noise which affects the quality of

the original signal. The PSNR is usually expressed

as the logarithmic decibel scale. A higher value in

PSNR represents better reconstructed or denoised im-

age. The PSNR is measured using Equation (10),

PSNR = 10log

(

MAX

MSE

), (10)

where MAX

represents the maximum intensity of the

image (255, for grayscale image) and MSE measures

the mean squared error between the original image

and the degraded image, as deﬁned in Equation (11),

MSE =

M × N

∑

i=0

∑

j=0

− v

)

, (11)

where u

is the original image, v

is the degraded

image and the size of the images is M × N.

4.2.2 Mean Structural Similarity (MSSIM)

One of the drawbacks of the PSNR measure is that it

relies on the mean square error for calculating the ra-

tio. Mean squared error considers only the differences

between isolated data points. To evaluate the perfor-

mance of a denoising method based on the degree of

structural similarity between the original and the re-

constructed image, the Structural SIMilarity (SSIM)

measure is used. The SSIM measure provides a bet-

ter assessment of an image restoration or denoising

method. The SSIM between two blocks is deﬁned in

Equation (12),

SSIM =

(2µ

+ c

)(2σ

+ c

)

(µ

+ µ

+ c

)(σ

+ σ

+ c

)

, (12)

where, x and y are two identical sized window or

patch, µ

and µ

are the averages of x and y, σ

and σ

are the variance of x and y and σ

is the co-variance.

The mean SSIM (MSSIM), averaged over all SSIM,

is used as for the quality measurement of a denoising

method.

4.3 Performance Evaluation using

PSNR

Table 3 shows the PSNR comparison of the proposed

method, the original non-local means, the variant of

non-local means and BM3D, on the Girl image. Ta-

ble 2 shows the average PSNR values over all images

in the Kodak image set, for various noise levels. The

performance of the proposed method is better than

the original non-local means method and its variant

for all noise levels. Yet, when compared to BM3D,

our proposed method managed to produce better re-

sults only when σ ≤ 80. The proposed method also

demonstrated better performance than existing meth-

ods on the average of all the noise levels used in our

experiments.

4.4 Performance Evaluation using

MSSIM

Table 3 shows the MSSIM comparison of the pro-

posed method, the original non-local means, the vari-

ant of non-local means and BM3D, on the Girl image.

Table 4 shows the MSSIM comparison over all im-

ages in the Kodak image set, for various noise levels.

VISAPP 2016 - International Conference on Computer Vision Theory and Applications

Table 1: PSNR comparison of the Girl image for the pro-

posed method and existing methods.

Noise NLM TS-NLM BM3D Proposed

10 33.92 33.93 35.42 35.61

20 31.83 32.01 33.46 33.60

30 29.43 29.70 31.03 31.12

40 28.47 28.96 29.88 30.04

50 26.64 27.20 28.21 28.27

60 25.12 25.77 26.53 26.60

70 24.78 25.24 25.88 26.03

80 23.69 24.46 25.33 25.50

90 23.15 24.04 24.95 24.81

100 22.91 23.88 24.43 24.28

Average 26.99 27.52 28.51 28.59

Table 2: PSNR comparison of the proposed method with

existing methods.

Noise NLM TS-NLM BM3D Proposed

10 32.61 32.63 34.05 34.27

20 30.77 30.94 32.25 32.43

30 28.58 28.83 29.80 29.95

40 27.02 27.47 28.19 28.33

50 24.88 25.54 26.07 26.09

60 23.93 24.66 25.38 25.46

70 23.24 24.02 24.74 24.91

80 22.90 23.56 24.46 24.65

90 22.21 23.18 24.25 24.13

100 21.98 22.83 23.97 23.84

Average 25.81 26.36 27.36 27.41

In terms of MSSIM, the performance of the proposed

method is consistent with PSNR, which means it is

better than the original non-local means and its vari-

ant for all noise levels. When compared to BM3D,

our proposed method managed to produce better re-

sults only when σ ≤ 80. On average across all noise

levels, the performance of proposed method has been

found to be better than existing methods.

4.5 Visual Quality

Figure 3 and Figure 4 shows the visual compari-

son of the proposed method with the original non-

local means (NLM), the two-stage non-local means

(TS-NLM) and the Block Matching and 3D Filtering

(BM3D) methods for noise level, σ = 20 and σ = 70

respectively. Figure 5 and Figure 6 shows the visual

comparison by zooming in on a particular region, the

face. From Figure 6, it can be noticed that the de-

noised output from the proposed method has fewer

noise artifacts remaining when compared to the other

methods. The blurring is also less in the denoised out-

Table 3: MSSIM comparison of the Girl image for the pro-

posed methods with existing methods.

Noise NLM TS-NLM BM3D Proposed

10 0.919 0.922 0.927 0.936

20 0.875 0.882 0.889 0.897

30 0.849 0.855 0.857 0.862

40 0.818 0.822 0.832 0.834

50 0.790 0.797 0.811 0.813

60 0.761 0.767 0.780 0.784

70 0.728 0.731 0.747 0.750

80 0.713 0.717 0.738 0.741

90 0.692 0.694 0.724 0.720

100 0.678 0.683 0.713 0.708

Average 0.782 0.787 0.802 0.804

Table 4: MSSIM comparison of the proposed methods with

existing methods.

Noise NLM TS-NLM BM3D Proposed

10 0.916 0.918 0.921 0.932

20 0.871 0.876 0.882 0.891

30 0.843 0.847 0.851 0.857

40 0.815 0.817 0.826 0.829

50 0.786 0.792 0.801 0.806

60 0.755 0.760 0.772 0.778

70 0.724 0.726 0.742 0.744

80 0.709 0.714 0.734 0.735

90 0.689 0.691 0.712 0.709

100 0.672 0.678 0.708 0.704

Average 0.777 0.782 0.795 0.798

put of the proposed method compared to NLM, TS-

NLM and BM3D.

4.6 Intensity Proﬁle

The image intensity proﬁle can help analyze how sim-

ilar the proﬁle of a denoised image is to that of the

original noise-free image. Figure 7 shows the chosen

horizontal scan line 100 from the Girl image. Figure

8 shows the intensity proﬁles of the true image, the

noisy image at noise level, σ = 70 and the proﬁles

of denoised images produced by the original NLM

scheme, the variant of NLM, BM3D and the proposed

method. The Pearson correlation coefﬁcient between

the original intensity proﬁle and the proﬁle of the

noisy and each of the denoised images is shown in

Table 5 (for σ = 70).

The intensity proﬁle of the proposed method

shows better preservation of edges and textures, rep-

resented as sharp changes in proﬁle graph. The origi-

nal non-local means method and its variant have more

noise artifacts remaining, as represented by the more

Non-local Means using Adaptive Weight Thresholding

(a) Noise Free (b) Noise (c) NLM (d) TS-NLM (e) BM3D (f) Proposed

Figure 3: Visual comparison of proposed method with existing method (σ = 20).

(a) Noise Free (b) Noise (c) NLM (d) TS-NLM (e) BM3D (f) Proposed

Figure 4: Visual comparison of proposed method with existing method (σ = 70).

(a) Noise Free (b) Noise (c) NLM (d) TS-NLM (e) BM3D (f) Proposed

Figure 5: Visual comparison (zoomed) of proposed method with existing method (σ = 20).

(a) Noise Free (b) Noise (c) NLM (d) TS-NLM (e) BM3D (f) Proposed

Figure 6: Visual comparison (zoomed) of proposed method with existing method (σ = 70).

Figure 7: Row number 100 of Girl image used for generating intensity proﬁle. Scan line shown as a black line.

Table 5: Pearson correlation coefﬁcient comparison of the

proposed method, the noisy image, the NLM method, vari-

ant of NLM and BM3D denoising scheme for noise σ = 70.

Noise NLM TS-NLM BM3D Proposed

0.680 0.975 0.980 0.988 0.990

jagged lines in the proﬁle graph, closer to the ori-

gin. When comparing the Pearson correlation coef-

ﬁcient, the correlation between the intensity proﬁle of

the original image and the proposed method is higher

compared to those of the other existing methods. It

shows that the proposed method has the closest re-

semblance to the intensity proﬁle of the original im-

age.

5 CONCLUSION

This paper proposed an improvement over the non-

local means method, the patch-based approach for

VISAPP 2016 - International Conference on Computer Vision Theory and Applications

(a) Original (b) Noise

(e) BM3D (f) Proposed

Figure 8: Intensity proﬁle comparison for the Girl image at scan line 100 (σ = 70).

denoising additive Gaussian noise in the spatial do-

main. The proposed method thresholds the weights

of the pixels deﬁned around a search area of the pixel

being denoised. The thresholded weights are used for

weighted averaging, whereby pixels below a deﬁned

cut-off weight are ignored. The cut-off weight is de-

Non-local Means using Adaptive Weight Thresholding

termined based on the noise level estimation of an

image. For a noise level, the patch and search win-

dow size are determined by a model, which is empir-

ically deﬁned through a learning approach. The pro-

posed method is applied in a two-step approach for

image denoising. The proposed method has demon-

strated better objective and subjective denoising per-

formance, compared to the original non-local means

algorithm and its variant. When compared to BM3D,

the state-of-the-art approach for image denoising, the

proposed method demonstrated better results when

σ ≤ 80.

ACKNOWLEDGEMENTS

This research is partially funded by the Natural Sci-

ences and Engineering Research Council of Canada

(NSERC). This support is greatly appreciated.

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